Total "person-hours" spent in scientific research. You get this from
the absolute population times the percentage employed in research times the
number of hours they work.

The above must be multiplied by an efficiency factor which reflects the
ever-increasing trend in the per-hour amount of knowledge they can generate
as a consequence of the increased effectiveness of the tools they use:
scientific equipment, computers, communication tools (for getting for
oneself, and giving to collegues, information relevant your mutual field of
study).

Some interesting factors to consider:

Technology enhances productivity, which supports both larger absolute
populations as well as a larger percentage of "knowledge workers", ie
scientists, as a fraction of the total population. Using technology
requires people trained in technology, which spawns an ever-increasing
knowledge distribution infrastructure, which is itself seminal to knowledge
generation. Competition in technology, for economic advantage as in the
current cultural model, makes generating new knowledge an economic survival
imperative--it is "self-forcing".

There may be other factors, but these above all seem like they would sort
of more-than-linearly boost each other's separate tendency to amplify the
rate of knowledge increase.